feat: persist active page in URL for shareable links

[DevLifeOfficial]

Summary

Persist the active playground page in the URL using the page query parameter.

Changes

• Read the initial page from the URL on load.
• Update the URL when switching between "Encoded sizes" and "Schema-first".
• Restore the active page from the URL on browser navigation.
• Fall back to sizes when the query parameter is missing or invalid.

Related Issue

#4 (comment)

Closes #4

Type of Change

• Bug fix
• New feature
• Refactor
• Documentation
• Chore / dependency update

Testing

• Verified that ?page=schema opens the Schema-first page.
• Verified that ?page=sizes (or no query parameter) opens the Encoded sizes page.
• Verified that switching pages updates the URL.
• Ran pnpm format.
• Ran pnpm lint.

Checklist

• Tests added or updated (optional)
• Documentation updated (if applicable)
• No breaking changes (or breaking changes are documented above)